Developer Utilities
Small developer utilities that save a trip to a random website. Encode and decode Base64, explain a regex, build UTM links, generate QR codes and vCards, and more — the everyday helpers. Free in your browser, and available by API when you need them in a script.
Developer Utilities
Multiplicative order calculator
find the order of a modulo n
POST /numth/multiplicative-order$0.002Developer Utilities
Baby-step giant-step calculator for discrete logarithms
POST /numth/baby-step-giant-step$0.002Developer Utilities
Count primitive roots modulo n
POST /numth/count-primitive-roots$0.002Developer Utilities
Complex root calculator
all nth roots of a complex number
POST /math/complex-root$0.002Developer Utilities
Condition number calculator
2-norm from singular values, free
POST /math/condition-number$0.002Developer Utilities
Cone surface area calculator
total, lateral and base area from r and l
POST /math/cone-surface-area$0.002Developer Utilities
Idempotents modulo n calculator
POST /numth/idempotents-mod-n$0.002Developer Utilities
Deterministic Miller–Rabin test
fixed witnesses, free
POST /numth/miller-rabin-deterministic$0.002Developer Utilities
Nth power residue checker
is a a k-th power mod prime p
POST /numth/power-residue-check$0.002Developer Utilities
Quadratic non-residues list mod p
all non-squares modulo odd prime
POST /numth/quadratic-nonresidues-list$0.002Developer Utilities
Solovay-Strassen primality test with a chosen base
POST /numth/solovay-strassen-test$0.002Developer Utilities
Conic section classifier
ellipse, parabola or hyperbola
POST /math/conic-sections$0.002Developer Utilities
Fermat pseudoprime checker for any base
POST /numth/fermat-pseudoprime-check$0.002Developer Utilities
Lucas pseudoprime checker
U-sequence test with parameters P,Q
POST /numth/lucas-pseudoprime-check$0.002Developer Utilities
Prime signature calculator
sorted factorization exponents
POST /numth/prime-signature$0.002Developer Utilities
Proth primality test
verify k × 2^n + 1 with a witness
POST /numth/proth-test$0.002Developer Utilities
Smallest prime factor calculator
least prime factor of n
POST /numth/smallest-prime-factor$0.002Developer Utilities
Complex conjugate calculator
flip the sign of the imaginary part
POST /math/conjugate$0.002Developer Utilities
Consecutive integers calculator
find n numbers that sum to a target
POST /math/consecutive-integers$0.002Developer Utilities
B-smooth numbers list
all B-smooth integers up to N
POST /numth/b-smooth-list$0.002Developer Utilities
Integer square root calculator
floor sqrt with Newton iteration
POST /numth/integer-square-root$0.002Developer Utilities
Mertens function calculator
compute M(n)
POST /numth/mertens-function$0.002Developer Utilities
Perfect cube checker
is n a cube and what is its root
POST /numth/perfect-cube-check$0.002Developer Utilities
Pollard's p−1 factorization
factor n with smoothness bound B
POST /numth/pollard-p-minus-one$0.002Developer Utilities
Squarefree Number Checker
Test an Integer Online
POST /numth/squarefree-check$0.002Developer Utilities
Unitary divisor sum calculator
compute sigma star of n
POST /numth/unitary-divisor-sum$0.002Developer Utilities
Convolution calculator
discrete convolution of two sequences, free
POST /math/convolution$0.002Developer Utilities
Coordinate distance calculator
Euclidean distance from x and y, free
POST /math/coordinate-distance$0.002Developer Utilities
Cototient calculator
compute n minus Euler's totient
POST /numth/cototient$0.002Developer Utilities
Highly Composite Number Checker
Test a Divisor Record
POST /numth/highly-composite-check$0.002Developer Utilities
Jordan totient calculator
J_k(n) from prime factors
POST /numth/jordan-totient$0.002Developer Utilities
Perfect number checker
is n equal to the sum of its proper divisors?
POST /numth/perfect-number-check$0.002Developer Utilities
Practical number checker
every smaller integer as distinct divisor sums
POST /numth/practical-number-check$0.002Developer Utilities
Sociable numbers checker
follow an aliquot sum cycle
POST /numth/sociable-numbers$0.002Developer Utilities
Totatives list calculator
find every integer coprime to n
POST /numth/totatives-list$0.002Developer Utilities
Corner point calculator
optimal LP vertex, free
POST /math/corner-point$0.002Developer Utilities
Calkin-Wilf fraction index
position of a reduced rational a/b
POST /numth/calkin-wilf-index$0.002Developer Utilities
Egyptian fraction term count
greedy unit-fraction expansion length
POST /numth/egyptian-fraction-length$0.002Developer Utilities
Quadrant finder
locate a point's quadrant or axis from x, y coordinates
POST /math/coordinate-grid$0.002Developer Utilities
Cosine calculator
cos(x) of an angle in radians, free
POST /math/cos$0.002Developer Utilities
cos⁻¹(x) calculator
arccosine in radians and degrees
POST /math/cos-1$0.002Developer Utilities
Bézout coefficients calculator
integers x, y with a·x + b·y = gcd
POST /numth/bezout-identity$0.002Developer Utilities
Two-coin representable checker
test a target amount
POST /numth/coin-representable-two$0.002Developer Utilities
Mediant of Two Fractions Calculator
POST /numth/mediant-fraction$0.002Developer Utilities
Negative Pell equation solver
solvability and minimal solution
POST /numth/negative-pell$0.002Developer Utilities
Pierce expansion calculator
alternating unit products for a fraction
POST /numth/pierce-expansion$0.002Developer Utilities
Pythagorean triples from a leg
list all integer triples for one side
POST /numth/pythagorean-from-leg$0.002Developer Utilities
cos(2θ) calculator
double-angle cosine from θ in radians
POST /math/cos-2-theta$0.002Developer Utilities
Hyperbolic cosine calculator
cosh(x) online, free
POST /math/cosh$0.002Developer Utilities
Distinct parts partition count
q(n) ways with unique summands, free
POST /numth/distinct-partitions$0.002Developer Utilities
Gaussian Integer Division Calculator
Quotient and Remainder
POST /numth/gaussian-integer-divide$0.002Developer Utilities
Gaussian integer factorization
factor a+bi into Gaussian primes
POST /numth/gaussian-integer-factor$0.002Developer Utilities
Goldbach partition count
count prime pairs for an even number
POST /numth/goldbach-partition$0.002Developer Utilities
Sum of three squares representation calculator
POST /numth/sum-three-squares-rep$0.002Developer Utilities
Sum of Two Squares Count
Calculate r₂(n)
POST /numth/sum-two-squares-count$0.002Developer Utilities
Waring problem representation
greedy sum of k-th powers
POST /numth/waring-representation$0.002Developer Utilities
Cosine similarity calculator
score between -1 and 1, free online
POST /math/cosine-similarity$0.002Developer Utilities
Cullen number generator
calculate n × 2^n + 1
POST /numth/cullen-number$0.002Developer Utilities
Digit factorial chain length calculator
POST /numth/digit-factorial-chain$0.002Developer Utilities
Factorion checker
is n equal to the sum of its digit factorials?
POST /numth/factorion-check$0.002